________________
D.E. Smith (pp.519-520), the well known American historian of mathematics, has found that Stifel was by no means the first to set forth the laws of indices. Probably the best of the statements regarding the laws of indices were of Nicolas Chuquet who expressed very clearly the addition and multiplication laws in Le Triparty en la Sciences des Nombres (1484 A.D.) from which Estienne de la Roche copied freely in his Larismethique of 1520 A.D.
Moreover, Rudolff's Kunstliche rechnung (1526 A.D.) where the double series is given and the multiplication law of indices is very clearly set forth, had great influence on Stifel.
After two decades of the publishment of Stifel's Arithmetica Integra, Forcadel (1565 A.D.) gave theory of indices with a statement that the idea was due to Archimedes. (Cf. Smith, p.522) [4.2] John Napier (1550 - 1617) was born at Merchiston (then near, now in Edinburgh) in Scotland. He became Baron of Merchistor. He was the eldest son of his father, Archibald Napier. It is remarkable that his father was only about 16 years old when he was born.
After working at least twenty years upon theory of logarithms, he published his work, in 1614 A.D., under the title Mirifici logarithmorum canonis descriptio which is briefly called the Descriptio. It was mainly aimed at simplifying expressions involving multiplication of sines.
In 1573 A.D., he married Elizabeth Sterling. She died in 1579 A.D. He married again Agnes Chisholm by whom he had 5 sons and 5 daughters. His second son, Robert Napier edited with ability his father's great work and published in 1619 A.D. under the title Mirifici logarithmorum canonis constructio which is briefly called the Constructio.
It is one of the greatest curisities of History of Mathematics that John Napier discovered logarithms (a) befor indices were used (Cf. Cajori, pp. 149 and 178) [b] and when the laws of indices laid down by Stifel were, if not completely
unknown, at least not formulated or not generally known (Cf. Bose, p.16 and Hooper, p. 174).
That a logarithm is simply an index was not observed long after Napier's invention. What, then, was his line of approach to logarithms.? To understand his approach, it should be remembered that (a) in his time and long afterwards, the sine of an angle (9) was not regarded
as a ratio but as the length of that semnichord of a circle of given radius
Arat Vacana, 15(4), 2003
65
Jain Education International
For Private & Personal Use Only
www.jainelibrary.org
